82.23.8 problem Ex. 9

Internal problem ID [18864]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems on chapter IV. page 49
Problem number : Ex. 9
Date solved : Tuesday, January 28, 2025 at 12:31:11 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} \left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 86

dsolve((8*diff(y(x),x)^3-27)*x=12*diff(y(x),x)^2*y(x),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {3 \,2^{{1}/{3}} x}{2} \\ y \left (x \right ) &= -\frac {3 \,2^{{1}/{3}} \left (i \sqrt {3}-1\right ) x}{4} \\ y \left (x \right ) &= \frac {3 \,2^{{1}/{3}} \left (1+i \sqrt {3}\right ) x}{4} \\ y \left (x \right ) &= \frac {8 x \sqrt {c_{1} x}-27 c_{1}^{2}}{12 c_{1}} \\ y \left (x \right ) &= \frac {-27 c_{1}^{2}-8 x \sqrt {c_{1} x}}{12 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 39.527 (sec). Leaf size: 15103

DSolve[(8*D[y[x],x]^3-27)*x==12*D[y[x],x]^2*y[x],y[x],x,IncludeSingularSolutions -> True]
 

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